We study intersection cohomology of character varieties for punctured Riemann surfaces with prescribed monodromies around the punctures. Relying on a previous result from Mellit [Mel20a] for semisimple monodromies we compute the intersection cohomology of character varieties with monodromies of any Jordan type. This proves the Poincaré polynomial specialization of a conjecture from Letellier [Let15].
Nous étudions la cohomologie d’intersection des variétés de caractères des surfaces de Riemann épointées, la monodromie autour des points enlevés étant fixée. En nous appuyant sur un résultat de Mellit [Mel20a] pour des monodromies semi-simples, nous calculons la cohomologie d’intersection des variétés de caractères avec des monodromies ayant un type de Jordan quelconque. Ceci prouve la spécialisation au polynôme de Poincaré d’une conjecture de Letellier [Let15].
Accepted:
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Keywords: Character varieties, intersection cohomology, parabolic Higgs bundles
Mot clés : Variétés de caractères, cohomologie d’intersection, fibrés de Higgs paraboliques
Mathieu Ballandras 1
@article{JEP_2023__10__141_0, author = {Mathieu Ballandras}, title = {Intersection cohomology of character varieties for punctured {Riemann} surfaces}, journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques}, pages = {141--198}, publisher = {\'Ecole polytechnique}, volume = {10}, year = {2023}, doi = {10.5802/jep.215}, language = {en}, url = {https://jep.centre-mersenne.org/articles/10.5802/jep.215/} }
TY - JOUR AU - Mathieu Ballandras TI - Intersection cohomology of character varieties for punctured Riemann surfaces JO - Journal de l’École polytechnique — Mathématiques PY - 2023 SP - 141 EP - 198 VL - 10 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.215/ DO - 10.5802/jep.215 LA - en ID - JEP_2023__10__141_0 ER -
%0 Journal Article %A Mathieu Ballandras %T Intersection cohomology of character varieties for punctured Riemann surfaces %J Journal de l’École polytechnique — Mathématiques %D 2023 %P 141-198 %V 10 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.215/ %R 10.5802/jep.215 %G en %F JEP_2023__10__141_0
Mathieu Ballandras. Intersection cohomology of character varieties for punctured Riemann surfaces. Journal de l’École polytechnique — Mathématiques, Volume 10 (2023), pp. 141-198. doi : 10.5802/jep.215. https://jep.centre-mersenne.org/articles/10.5802/jep.215/
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